EU also threatened Belarus with more sanctions following the death of a 31-year-old protester who died in the hospital after being allegedly beaten by the police.
Thousands of people have taken to the streets of Minsk and other Belarusian cities after the death of a 31-year-old protester who died in hospital after what demonstrators say was a severe beating by security forces.
The man's death on Thursday came after more than three months of mass anti-government protests that were sparked by official election results that gave authoritarian President Alexander Lukashenko a sixth term in office.
Opposition leaders and some poll workers say the results were manipulated, and protesters have been calling for Lukashenko's resignation.
The Interior Ministry on Friday denied responsibility for Bondarenko's death, saying he was killed due to a scuffle with civilians.
The state Investigative Committee alleged Bondarenko was drunk, which was disputed in local media, citing the official medical report into his death.
The death is the latest flashpoint in months of mass protests against Lukashenko following a disputed presidential election in August. The opposition says Lukashenko rigged the vote to secure a sixth successive term.
Lukashenko denies electoral fraud and, buoyed by support from traditional ally Russia, has shown little inclination to step down.
A violent crackdown prompted a new round of Western sanctions on Minsk.
The European Union called the death "an outrageous and shameful result of the actions by the Belarusian authorities" who have "directly and violently carried out repression of their own population."
The bloc, which has blacklisted some Belarusian officials, threatened further sanctions.
Rupert Colville, the United Nations human rights spokesperson, called for a "thorough, transparent and independent investigation."
Videos posted by Belarusian media on Friday showed people standing along roads, near universities, factories and hospitals with white-red-white flags in their hands and portraits of Bondarenko.
In a video from the courtyard where Bondarenko was detained, hundreds of people stood in a minute of silence and then chanted: "We will not forget, we will not forgive."
"It's impossible to bear, what they did. Everybody is crying here," said a participant in one of the human solidarity chains in Minsk.
The news outlet Nasha Niva reported that police had detained protesters in at least four towns.